A new version of Bishop frame and an application to spherical images
type: Item
instance of: scholarly article
title: A new version of Bishop frame and an application to spherical images
zbMATH Open document ID: 1207.53003
author: Süha Yılmaz
author: Melih Turgut
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-09-01T00:00:00Z
review text: A classical Bishop frame is a moving frame of a curve in Euclidean three space [\textit{R. L. Bishop}, Am. Math. Mon. 82, 246--251 (1975; Zbl 0298.53001)] with the following properties. Considering a curve parametrized by arclength \(s\), the first vector is the unit tangent vector \(T(s)\), the second and third vector \(M_1(s),M_2(s)\) are selected arbitrarily so that \((T(s), M_1(s), M_2(s))\) is an orthonormal frame and the (skew symmetric) frame equations read \(T'=k_1M_1+k_2M_2, M_1'=-k_1T, M_2'=-k_2T\). In the present paper the authors introduce an other version of a Bishop frame using the binormal vector shared with the Frenet frame. The relations to the Frenet frame and the classical Bishop frame are discussed as well as the spherical images. As applications, general helices and slant helices (regular curves the principal normals of which form a constant angle with a fixed direction) are discussed.
reviewed by: Friedrich Manhart
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 5777351
zbMATH Keywords: Bishop frame
zbMATH Keywords: general helix
zbMATH Keywords: slant helix
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.06.012
OpenAlex ID: W1997099988
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DOI: 10.1016/J.JMAA.2010.06.012
description: scientific article; zbMATH DE number 5777351